Dark Haloes and the Kinematics of Disc Galaxies

The decomposition of the 21 cm rotation curve of galaxies into contribution from the disc and dark halo is challenging and depends on the adopted mass to light ratio (M/L) of the disc. There are several traditional methods of determining the stellar M/L but they remain uncertain. One method is the maximum disc hypothesis, where we adopt the largest M/L such that the disc’s contribution to the observed rotation curve does not anywhere exceed the observed rotation curve. However, the maximality of the disc has not been conclusively proven. Another method used to estimate the M/L is from stellar population synthesis models, but these have significant assumptions involved such as the star formation history, the stellar initial mass function, chemical enrichment history etc. A more direct way of calculating the stellar M/L is by measuring the surface mass density of the disc. For a given vertical density distribution, the Jean’s equation in the vertical direction gives a rather simple relation between the disc surface mass density (Σ), vertical velocity dispersion (σz), and the scale height (hz). Therefore, once we have adopted a density model for the disc, given the σz and hz for a galaxy, we can determine the Σ. These densities can be used along with the surface brightness profile of the galaxy to determine the M/L. This is an observationally determined M/L without as many assumptions involved as in the other techniques. Previous studies such as the DiskMass survey (Bershady et al. 2010a) and work by Herrmann et al. (2008) have used this method to conclude that galaxy discs are submaximal. The DiskMass survey used IFU spectroscopy and Herrmann et al. (2008) used planetary nebulae (PNe) to trace the kinematics of the discs of a sample of nearby spirals. Both these independent studies, using different tracers of the disc kinematics, concluded that galaxy discs are submaximal. However, there is a conceptual problem that these studies were not able to address. Measuring the surface density of the disc requires a velocity dispersion and a disc scale height but they must be for the same population of the tracers. Discs of spirals contain stars (and PNe) of all ages. The younger stars (ages ~ 3 Gyr) have a relatively small scale height and velocity dispersion, compared to the older, kinematically hotter disc stars (ages ~ 3 – 10 Gyr). Since it is not possible to measure the scale height directly in face-on discs, we need to estimate it statistically using I-band and near-IR photometric data for edge-on galaxies; these estimates are weighted towards the scale height of the old disc, away from the dust plane of these galaxies. The spectra of the integrated light of the disc, which we use to measure the vertical velocity dispersion, come from the luminosity-weighted stellar population of the disc and contain a considerable contribution from the kinematically colder, younger disc population. Failing to separate out this younger component will lead to underestimating the velocity dispersion of the old disc. The surface density of the disc is therefore underestimated, and even if a disc in truly maximal disc, it will appear to be submaximal. In this thesis, we use a sample of K-giants in the solar neighbourhood to establish that there really do exist two thin disc components: a kinematically cold component with a small dispersion and a hotter component with about twice the dispersion. We establish that assuming a single kinematically homogeneous population of stars will underestimate the surface mass density by a factor of 2. This factor will play a huge factor in whether a galaxy is classified as being maximal or submaximal. We then use a sample of three nearby, relatively face-on spirals (NGC 628, NGC 6946, and NGC 5457) to extract the vertical velocity dispersion of the hot thin disc. We use absorption line spectra from the VIRUS-W instrument at McDonald observatory and PNe observed with the Planetary Nebula Spectrograph to trace the kinematics of the discs of these galaxies. In all three galaxies, using these two kinematic tracers, we were able to extract the velocity dispersion of the hot component, which we then used along with the scale height (for the same component) to determine the surface mass densities. The central surface mass densities that we derive are typically at least a factor of 2 higher than previous studies. We find that the vertical velocity dispersion of the hot component falls exponentially with twice the radial scale length of the galaxy as a function of radius. This implies that these galaxies have a constant scale height and constant M/L. We used available photometric data to calculate the M/L in each radial bin where we determined the dynamical surface densities. We believe that this is the first dynamical study that gives the observed M/L in different radial bins for these nearby disc galaxies. We find all three of our analysed galaxies to be maximal. The baryons dominate in the inner parts of these galaxies, with the dark halo contributing minimally to the rotation curve